class: center, top, .title-slide, title-slide # Biostats Lecture 5:
Statistical Hypothesis Testing ## Public Health 783 ### Ralph Trane ### University of Wisconsin–Madison
### Fall 2019 --- # Recap Random variables Distributions Estimators Estimators are random variables! (for example, the average is a random variable) --- layout: true # Statistical Hypothesis Testing --- **Scenario**: We've been playing a simple game. Everytime you roll a six, I pay you a dollar. Everytime I roll a six, you pay me a dollar. I've had crazy good luck, and by the end of the day won a lot of money from you. -- You accuse me of cheating, and demand to test the dice I've been using! I agree to let you test them, but ONLY if you do it in a sound, statistical manner. How to go about that? -- You decide to roll the dice `\(3\)` times each, for a total of `\(27\)` rolls. You assume they'll all behave the same, so the probability of rolling a six is the same for all three dice. --- **Setup**: Let `\(X_1, X_2, ..., X_{27}\)` be the outcomes of the thirty "trials". Each trial consists of rolling a die, and check if it's a six or not. If it's a six, we'll call it a success, if not we'll call it a failure. I.e. `\(X_i \sim\)` -- `\(\text{Bernoulli}(\pi)\)`. *IF* the dice are fair, `\(P(X_i = 1) = 1/6\)` for all `\(i = 1,2,...,27\)`. *IF* the dice are fair, we would expect to roll a `\(6\)` close to `\(\frac{1}{6}\cdot 27 = 6\)` times, i.e. about `\(5\)` of the `\(X\)`'s should be `\(1\)`'s. What would cause you to reject the idea that the dice are fair? -- If we see way more than `\(6\)` sixes. What would be "way more"? `\(7\)`? `\(8\)`? `\(17\)`? --- In terms of probabilities: what is the *probability* of observing at least `\(10\)` sixes *IF* the `\(P(X_i = 1) = \frac{1}{6}\)`? * if the probability is small, `\(10\)` is a lot of sixes * if the probability is large, `\(10\)` is a reasonable number of sixes First, introduce the random variable `\(Y =\)` number of sixes `\(= X_1 + X_2 + ... X_{27}\)`. The probability of observing more than `\(10\)` sixes is `\(P(Y \ge 10)\)`. To find this, we need the distribution of `\(Y\)`, which is -- `\(\text{Binomial}(27, \pi)\)`, where `\(\pi\)` is the probability of rolling a six. --- *IF* the dice are fair, `\(\pi = \frac{1}{6}\)`. So *IF* the dice are fair, the distribution of `\(Y\)` looks like this: <center>
</center> --- The probability we want to find is the red area below. We will do this in SAS in just a second. The result is 0.00261. <center>
</center> --- This means that *IF* the true probability of rolling a six with these dice is indeed `\(\frac{1}{6}\)`, the probability of rolling `\(10\)` or more sixes is `\(0.00261\)`. This probability is called the *p-value* for the test `\(H_0: \pi = 1/6\)` when testing against `\(H_A: \pi > 1/6\)`. Is this small enough to convince you that the true probability is *NOT* `\(\frac{1}{6}\)`? --- </br> </br> </br> </br> .center[ **In SAS.** ] --- ## Different (but the same) approach Instead of looking at `\(Y\)` (number of sixes), look at the proportion of sixes. I.e. `$$\hat{p} = \frac{Y}{n} = \frac{1}{27}(X_1 + ... + X_{27}) = \frac{1}{27} \sum_{i=1}^{27} X_i$$` This is an average, so CLT tells us it's normally distributed around the true value of `\(\pi\)`, and variance `\(\frac{\text{Var}(X_i)}{n} = \frac{\pi(1-\pi)}{27}\)`. We reject the idea that the true value of `\(\pi\)` is `\(\frac{1}{6}\)` when `\(\hat{p}\)` is "far from" `\(\frac{1}{6}\)`. I.e. when `\(\hat{p} - \frac{1}{6}\)` is large. When this is large, so is `\(Z = \frac{\hat{p}-1/6}{\text{SD}(\hat{p})}\)`. If we pretend `\(\pi = \frac{1}{6}\)`, then `\(Z \sim N(0,1)\)`! If we pretend `\(\pi = \frac{1}{6}\)`, then `\(\text{SD}(\hat{p}) = \sqrt{\text{Var}(\hat{p})} = \sqrt{\frac{1/6 \cdot (1-1/6)}{27}}\)`, and so we can actually calculate `\(z_{obs}\)`, the observed value of `\(Z\)`. --- ## Different (but the same) approach So, `\begin{align*} \text{p-value} &= P(\hat{p} > p_{obs}) \\ &= P\left(\frac{\hat{p} - 1/6}{\text{SD}(\hat{p})} > \frac{p_{obs} - 1/6}{\sqrt{1/6 \cdot (1-1/6)/27}} \right) &= P(Z > 2.84019) \end{align*}` --- So we found our p-value as the area depicted below. Turns out, this is 0.00225. <img 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" width="450" height="300" style="display: block; margin: auto;" /> This strategy can be used every time we the quantity of interest in follows a (at least approximately) normal distribution. Subtract the mean and divide by the standard deviation to get the standard normal. Then find the probability. --- ## Group Comparison Two groups, 15 observations in each group. Want to test `\(H_0: \mu_X = \mu_Y\)` against `\(H_A: \mu_X \neq \mu_Y\)`. <img src="data:image/png;base64,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" width="450" height="300" style="display: block; margin: auto;" /> --- Natural to look at `\(\bar{X} - \bar{Y}\)`. If `\(n\)` is "large enough", both of these quantities are normally distributed. From last week, normal minus normal is normal. So `\(\bar{X} - \bar{Y}\)` is normal! Next question: exactly what normal would it be *IF* we pretend the null hypothesis is true? Mean: `\(E(\bar{X} - \bar{Y}) = E(\bar{X}) - E(\bar{Y})=\)` -- `\(\mu_X - \mu_Y =\)` -- `\(0\)` Variance (assuming independence): `\(\text{Var}(\bar{X} - \bar{Y}) =\)` -- `\(\text{Var}(\bar{X}) + \text{Var}(\bar{Y}) = \frac{\sigma_X^2}{n_X} + \frac{\sigma_Y^2}{n_Y}\)`. So `\(Z = \frac{\bar{X} - \bar{Y}}{\text{SD}(\bar{X} - \bar{Y})} = \frac{\bar{X} - \bar{Y}}{\sqrt{\text{Var}(\bar{X} - \bar{Y})}} \sim N(0,1)\)`. What's the problem here? -- We don't know `\(\sigma_X^2\)` or `\(\sigma_Y^2\)`! --- Luckily, we can simply *estimate* both, and plug them in. When we do this, the result no longer follows a standard normal distribution... -- BUT it follows a particular `\(t\)`-distribution. How to calculate the exact degrees of freedom is a bit tricky, but it can be done. **For the patient type:** The degrees of freedom is `\begin{align*} \text{df} &= n_X + n_Y - 2 \end{align*}` if we are willing to assume `\(\sigma_X^2 = \sigma_Y^2\)`. In this case we would use `\(s_X^2 = s_Y^2 = \frac{1}{n_X + n_Y - 2}\left(\sum_{i=1}^{n_X} (x_i - \bar{x})^2 + \sum_{i=1}^{n_Y} (y_i - \bar{y})^2\right)\)`. --- If you're not willing to assume `\(\sigma_X^2 = \sigma_Y^2\)`, the degrees of freedom is `\begin{align*} \text{df} &= \frac{\left[\frac{s_X^2}{n_X} + \frac{s_Y^2}{n_Y}\right]^2}{\frac{(s_X^2/n_X)^2}{n_X - 1} + \frac{(s_Y^2/n_Y)^2}{n_Y - 1}}, \end{align*}` and we would then use the regular sample variances as estimates: `\begin{align*} s_X^2 &= \frac{1}{n_X - 1} \sum_{i=1}^{n_X} (x_i - \bar{x})^2 \\ &\\ s_Y^2 &= \frac{1}{n_Y - 1} \sum_{i=1}^{n_Y} (y_i - \bar{y})^2 \end{align*}` --- **For the not so patient type:** Don't worry about it, you'll use software to calculate this. HOWEVER, you will need to know WHEN you can assume equal variance.